Scattering in graphene quantum dots under generalized uncertainty principle

In this article, the Dirac electron scattering problem on circular barrier of radius [Formula: see text] is studied under the generalized uncertainty principle (GUP). The expressions of scattering coefficients, scattering cross-section and scattering efficiency of massless Dirac particle are obtained by solving the massless Dirac equation under GUP and discussed by numerical methods. It shows that the scattering coefficient, the scattering cross-section, and the scattering efficiency depend explicitly on the GUP parameter [Formula: see text]. For the scattering coefficient [Formula: see text], GUP may cause slight shift in the oscillation position of [Formula: see text] and make some peaks value of [Formula: see text] smaller. For scattering cross-section and scattering efficiency, GUP may also lead to slight shift in their oscillation position and increase of amplitude when the GUP parameter increases.

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Acoustic Scattering Cross Sections of Smart Obstacles: A Case Study

Communications in Computational Physics ◽

10.4208/cicp.120310.261110a ◽

2011 ◽

Vol 10 (3) ◽

pp. 672-694

Author(s):

Lorella Fatone ◽

Maria Cristina Recchioni ◽

Francesco Zirilli

Keyword(s):

Cross Section ◽

Cross Sections ◽

Space Shuttle ◽

Scattering Problem ◽

Plane Waves ◽

Acoustic Scattering ◽

Scattering Cross Section ◽

Scattering Cross ◽

Scattering Cross Sections

AbstractAcoustic scattering cross sections of smart furtive obstacles are studied and discussed. A smart furtive obstacle is an obstacle that, when hit by an incoming field, avoids detection through the use of a pressure current acting on its boundary. A highly parallelizable algorithm for computing the acoustic scattering cross section of smart obstacles is developed. As a case study, this algorithm is applied to the (acoustic) scattering cross section of a “smart” (furtive) simplified version of the NASA space shuttle when hit by incoming time-harmonic plane waves, the wavelengths of which are small compared to the characteristic dimensions of the shuttle. The solution to this numerically challenging scattering problem requires the solution of systems of linear equations with many unknowns and equations. Due to the sparsity of these systems of equations, they can be stored and solved using affordable computing resources. A cross section analysis of the simplified NASA space shuttle highlights three findings: i) the smart furtive obstacle reduces the magnitude of its cross section compared to the cross section of a corresponding “passive” obstacle; ii) several wave propagation directions fail to satisfactorily respond to the smart strategy of the obstacle; iii) satisfactory furtive effects along all directions may only be obtained by using a pressure current of considerable magnitude. Numerical experiments and virtual reality applications can be found at the website: http://www.ceri.uniromal.it/ceri/zirilli/w7.

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Mass Determination by Direct Measurement of Electron Scattering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100114827 ◽

1975 ◽

Vol 33 ◽

pp. 240-241

Author(s):

M. K. Lamvik ◽

A. V. Crewe

Keyword(s):

Cross Section ◽

Electron Scattering ◽

Mass Density ◽

Variable Mass ◽

Scattering Cross Section ◽

Mass Determination ◽

Number Density ◽

Cross Sectional ◽

Thin Slice ◽

Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

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